# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

### Compose Your Message

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Re: Spherical Trig
From: Bill B
Date: 2005 Apr 5, 20:59 -0500

```Thank you NS and Dan,

One of those queries that raises the question as to what I was thinking, or
was I thinking at all? ;-)

If, for example, I had two points on the equator, one at 90d W, another at
90d E, and a third at the pole; I would have 90d each for the equator
angles, and another 180d for the LHA/t angle.  Hence 360d total or 2 pi
radians.

If I had LHA approaching 360d, I would have 359.xxx plus 2X 90.yyy, so close
to 540d or 3 pi radians.

As a follow up question:
Dan stated, "The sum of the angles of a spherical triangle is between pi and
3 pi radians (180 deg and 540 deg)."  Focusing on the words "is between"
does that literally mean the lower limit can approach 180d and the upper
limit approach 540d, or can the sums actual equal either 180d or 540d?

Bill

> On Apr 5, 2005, at 4:08 PM, n s gurnell wrote:
>
>> Re Bill's question about the angles in a spherical triangle.
>> Sixty years ago the exams called "Principles for Second Mates" used to
>> have a
>> question:- "What is Spherical Excess?" I've forgotten the exact answer
>> but
>> someone might know. Old Timer
>
> The sum of the angles of a spherical triangle is between pi and 3 pi
> radians (180 deg and 540 deg). The amount by which it exceeds 180 deg
> is called the spherical excess and is denoted E. The difference between
> 2 pi radians (360 deg) and the sum of the side arc lengths a, b, and c
> is called the spherical defect and is denoted D.
>
> Girard's formula:
>
> Spherical Excess = E = A + B + C - pi
> where A,B, and C are angles measured in radians
> Surface Area = E * R^2
> where R is the radius of the sphere
>
> Dan

```
Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)